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United States Patent |
6,088,646
|
Wiel
|
July 11, 2000
|
Fuzzy logic antiskid control system for aircraft
Abstract
An antiskid control system for aircraft braking consisting of an iterative
system having inputs including wheel speed, time since touchdown and the
value of the control current generated by the previous iteration.
Utilizing the previous value and applying fuzzy logic rules, the system
modifies itself to adjust for variations in the coefficient of friction
between the wheels and the runway.
Inventors:
|
Wiel; Colin T. (Kent, WA)
|
Assignee:
|
The Boeing Company (Seattle, WA)
|
Appl. No.:
|
736650 |
Filed:
|
October 25, 1996 |
Current U.S. Class: |
701/77; 244/111; 303/126 |
Intern'l Class: |
B60T 007/12; G06F 017/00 |
Field of Search: |
701/77,70,71
303/100,194,126
244/111
|
References Cited
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|
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|
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|
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|
4842342 | Jun., 1989 | Takahashi et al. | 303/102.
|
4852007 | Jul., 1989 | Yasunobu et al. | 364/426.
|
5001640 | Mar., 1991 | Matsumoto et al. | 364/426.
|
5018689 | May., 1991 | Yasunobu et al. | 246/182.
|
5019774 | May., 1991 | Rosenberg | 324/174.
|
5024491 | Jun., 1991 | Pease, Jr. et al. | 303/93.
|
5050940 | Sep., 1991 | Bedford et al. | 303/100.
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5082081 | Jan., 1992 | Tsuyama et al. | 180/197.
|
5173860 | Dec., 1992 | Walenty et al. | 364/426.
|
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|
5229955 | Jul., 1993 | Nishiwaki et al. | 364/550.
|
5245695 | Sep., 1993 | Basehore | 395/3.
|
5289095 | Feb., 1994 | Ushiyama | 318/560.
|
5302007 | Apr., 1994 | Morita et al. | 303/9.
|
5358317 | Oct., 1994 | Cikanek | 303/100.
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5388895 | Feb., 1995 | Negrin | 303/103.
|
5397973 | Mar., 1995 | Dommermuth | 318/628.
|
5411323 | May., 1995 | Takahashi et al. | 303/20.
|
5416709 | May., 1995 | Yeh et al. | 364/426.
|
5425131 | Jun., 1995 | Basehore | 395/3.
|
5459816 | Oct., 1995 | Basehore et al. | 395/3.
|
5474368 | Dec., 1995 | Sano | 303/163.
|
5483446 | Jan., 1996 | Momose et al. | 364/424.
|
5497063 | Mar., 1996 | Day et al. | 318/610.
|
5497449 | Mar., 1996 | Miyazawa | 395/61.
|
5524176 | Jun., 1996 | Narita et al. | 395/22.
|
5539642 | Jul., 1996 | Wiel | 364/426.
|
Primary Examiner: Cuchlinski, Jr.; William A.
Assistant Examiner: Pipala; Edward
Attorney, Agent or Firm: Gardner; Conrad O.
Parent Case Text
This application is a continuation of prior copending application Ser. No.
08/350,927, filed Dec. 7, 1996, now abandoned.
Claims
What is claimed:
1. An antiskid brake control system for an aircraft for providing an
antiskid control current to an antiskid valve comprising in combination:
an iterative control system responsive to wheel speed and time since
touchdown;
said iterative control system further responsive to the antiskid control
current generated by a previous iteration;
said iterative control system utilizing four fuzzy inference systems for
determining the values of four intermediate variables to provide said
antiskid control current to the antiskid valve.
2. The antiskid brake control system of claim 1 wherein said four
intermediate variables are reference velocity rate limit, change in
antiskid current, gain, and change in base limit.
3. A method for estimating aircraft velocity comprising the steps of:
reading wheel speed;
comparing a subsequent wheel speed reading with a previous reference
velocity; and
limiting the change in wheel speed to an amount determined by fuzzy
inference.
4. An antiskid control system for an aircraft for providing an antiskid
control current for an antiskid valve comprising in combination:
an iterative system responsive to wheel speed, time since touchdown and the
antiskid control current generated by a previous iteration for providing
said antiskid control current;
fuzzy logic rules for adjusting said iterative system for variation in the
coefficient of friction between the wheels of said aircraft and the
runway.
5. The method according to claim 3 wherein said fuzzy interference utilizes
current base limit and time since touchdown as inputs.
6. An antiskid brake control system for aircraft utilizing a fuzzy system
to calculate reference velocity limit;
said fuzzy inference system receiving base current limit and time since
touchdown as inputs, and providing reference velocity rate limit as
output.
7. An antiskid brake control system for aircraft utilizing a fuzzy system
to calculate Gain;
said fuzzy inference system receiving base current limit as input and
giving gain as output.
8. An antiskid brake control system for aircraft utilizing fuzzy system to
calculate base current limit;
said fuzzy inference system receiving deviation of antiskid current from
base limit, time since skid, wheelspeed error, and derivative of
wheelspeed as inputs, and giving change in base limit as output.
9. A method of antiskid brake control for an aircraft comprising the steps
of:
calculating a reference velocity by fuzzy inference;
calculating decision variables wheelspeed error, rate of change of
wheelspeed error, derivative of wheelspeed, second derivative of
wheelspeed, time since touchdown, time since skid, and deviation between
base current limit and antiskid current limit;
calculating .DELTA.base current by fuzzy inference;
calculating .DELTA.antiskid current by fuzzy inference;
calculating gain by fuzzy inference; and
limiting antiskid current to base limit level.
10. An antiskid brake control system for an aircraft for providing an
antiskid control current to an antiskid valve comprising in combination:
an iterative control system responsive to wheel speed and time since
touchdown;
said iterative control system further responsive to the antiskid control
current generated by a previous iteration;
said iterative control system utilizing four fuzzy inference systems for
determining the values of four intermediate variables to provide said
antiskid control current to the antiskid valve; and
wherein said four intermediate variables are reference velocity rate limit,
change in antiskid current, gain and change in base limit.
Description
FIELD OF THE INVENTION
The present invention relates to an antiskid brake control system and more
particularly to an antiskid brake control system utilizing fuzzy logic
rules utilizing time since touchdown as an input and further responsive to
antiskid control current generated by the previous iteration.
BACKGROUND OF THE INVENTION
Fuzzy inference means has heretofore been utilized in a detecting road
surface frictional coefficient in automotive applications as shown in U.S.
Pat. No. 5,229,955 to Nishiwaki et al.
U.S. Pat. No. 4,843,342 to Takahashi et al. discloses an antiskid brake
control system using fuzzy logic rules. It requires a wheel speed input
and sensor for vehicle body behavior (the exemplary system uses
acceleration). In contrast, the present system hereinafter described
utilizes only wheel speed and a clock; all other quantities are derived
therefrom. U.S. Pat. No. 5,001,640 to Matsumoto et al. suggests a servo
control system consisting of a controlled object, an actuator for
controlling it, a sensor monitoring the controlled quantity, and a control
device employing fuzzy reasoning. It is implied that the inputs are
limited to reduce the required calculations and improve the response time
of the system. The exemplary system in Matsumoto et al. is an antiskid
brake control system for an automobile. However, instead of monitoring
only the controlled quantity as hereinafter described, the system shown in
Matsumoto et al. uses both wheel speeds and applied hydraulic brake
pressures as inputs.
SUMMARY OF THE INVENTION
An aircraft brake antiskid system employing fuzzy logic in an iterative
system. Parameters include wheel speed, time since touchdown, and value of
the control current generated by a previous iteration.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of the present aircraft brake antiskid system
including an algorithm diagram;
FIG. 2 and FIG. 3 are diagrams of the reference velocity fuzzy sets
utilized in the present system;
FIGS. 4 A, B, and C are diagrams of the antiskid current fuzzy sets;
FIG. 5 is a diagram showing gain fuzzy sets for base limits that are small,
medium, and large; and,
FIGS. 6 A, B, C, and D are diagrams illustrative of the base limit fuzzy
sets utilized in the present antiskid system of FIG. 1.
DETAILED DESCRIPTION OF THE INVENTION
Introduction
The antiskid system controls the amount of electric current sent to an
electronic servo valve, which in turn meters hydraulic pressure from the
brakes of the aircraft. Skids are detected by a sudden decrease of wheel
speed. When a skid is detected, the controller immediately sends a current
to the antiskid valve to release the pressure in that brake.
Currently existing systems serve this objective, but not perfectly. The
present fuzzy logic antiskid system was developed in order to yield better
braking efficiencies under a wide range of conditions.
Description Of Fuzzy Inference Process
The four fuzzy inference systems which are utilized in the present fuzzy
antiskid algorithm utilize the product-sum-gravity method of inference,
also called sum-product inference. Each takes multiple inputs, x.sub.1
through x.sub.n, and calculates a single output, y.
The algorithm is described hereinafter. This description is divided into
two sections, viz. Knowledge Base, and Inferencing. The former describes
how the rules of inference are defined mathematically, and the latter
describes how the knowledge base is accessed to make a decision.
Knowledge Base
The knowledge of a fuzzy inference system is stored in a set of fuzzy if .
. . then rules. Each rule is of the form:
If x.sub.1 is A.sub.i1 AND x.sub.2 is A.sub.i2 and . . . x.sub.n is
A.sub.in THEN y is B.sub.i. The rule can be divided into an antecedent
part, "If x.sub.1 is A.sub.i1 AND x.sub.2 is A.sub.i2 and . . . x.sub.n is
A.sub.in ", and a consequent part, "THEN y is B.sub.i ". Here A.sub.ij 's
are fuzzy sets. The B.sub.i 's are scalar values.
A fuzzy set is a set which allows membership values in the [0,1] interval.
(Conventional set theory allows membership values of 0 and 1, only.) The
fuzzy set is defined on a universal set by a membership function which
maps all elements of the universal set to the [0,1] interval:
.mu.A.sub.ij (x): X.fwdarw.[0.1].
Typically, a rule base will contain two to 50 rules, although larger rule
bases have been used for some highly complex applications. A complete rule
base has the form:
R.sub.1 : If x.sub.1 is A.sub.11 AND x.sub.2 is A.sub.12 and . . . x.sub.n
is A.sub.1n THEN y is B.sub.1
R.sub.2 : If x.sub.1 is A.sub.21 AND X.sub.2 is A.sub.22 and . . . x.sub.n
is A.sub.2 n THEN y is B.sub.2
R.sub.m : If x.sub.1 is A.sub.m1 AND X.sub.2 is A.sub.m2 and . . . x.sub.n
is A.sub.mn THEN y is B.sub.m
Inferencing
In the fuzzy inference process, all of the rules come into play to some
degree. The degree to which a rule comes into play, called the weight, is
equal to the degree to which the antecedent condition of the rule is
satisfied. The weights of the rules are then used in taking the weighted
average of the outputs of the rules.
The weight of a rule is determined as:
W.sub.i =.mu.A.sub.i1 (x.sub.1) x .mu.A.sub.i2 (x.sub.2) x . . .
x.mu.A.sub.in (x.sub.n)
The inference output, y, is calculated as follows:
##EQU1##
Algorithm Description
The Fuzzy antiskid algorithm as shown in FIG. 1 receives wheel speed as an
input, and determines the level of current to be sent to the antiskid
valve. The algorithm uses four separate fuzzy inference systems to
determine the values of four intermediate variables which are then used to
determine the antiskid current level. The four intermediate variables are
reference velocity rate limit, change in antiskid current (before gain and
limit are applied), gain, and change in base limit.
The reference velocity rate limit is used to establish a reference
velocity. By comparing the wheel speed to the reference velocity, skids
are recognized. The error, which is the difference between the reference
velocity and the wheel speed, indicates the depth of a skid.
The error, along with the derivative of error and second derivative of
wheel speed, are used to determine the change in antiskid current. This
value is then multiplied by a gain and added to the previous antiskid
current. The antiskid current is then limited to a maximum of 55 mA and a
minimum of the base limit level.
The gain is determined by how slippery the runway is. The base limit level
is determined primarily by the deviation, which is the difference between
the antiskid current level and the base limit itself. The amount of time
since a skid, the error, and the derivative of wheel speed are also used
in determining the base limit level.
The fuzzy antiskid algorithm can be divided into eight functional
components, each of which is discussed below.
1) Estimate Reference Velocity (Fuzzy Inference)
2) Calculate Decision Variables
3) Determine Change in Antiskid Current (Fuzzy Inference)
4) Determine Gain (Fuzzy Inference)
5) Determine Change in Base Limit (Fuzzy Inference)
6) Sum and Limit Base Limit
7) Sum and Limit Antiskid Current
8) Send Current to Valve
Estimate Airplane Velocity (Fuzzy Inference)
The airplane velocity is estimated to provide a reference to which wheel
speed can be compared to recognize a skid (reference velocity). This
reference velocity is estimated based solely on the wheel speed, as no
other input is provided to the antiskid system. Each cycle of the
algorithm, after the wheel speed is read, the previous reference velocity
is compared to the new wheel speed reading. Based on this comparison, a
new reference velocity is determined. The approach taken is described as
follows:
If the reference velocity is less than the wheel speed, the reference
velocity should be increased to match the wheel speed, because in general
the wheels can not go faster than the airplane.
If the reference velocity is greater than or equal to the wheel speed then
the new reference velocity is taken as the wheel speed, provided that the
decrease in reference velocity does not exceed a limiting value, the
reference velocity rate limit. If the decrease in reference velocity would
exceed the reference velocity rate limit, then it is assumed that the
airplane is skidding. In this case the new value of reference velocity is
taken as the previous value of the reference velocity less the reference
velocity rate limit.
The reference velocity rate limit is determined based on how slippery the
runway is. A fuzzy inference system is used.
The fuzzy inference system uses the strategy that if the base limit is high
then the runway is slippery, and the reference velocity should be
decreased slowly. If the base limit is low then the runway is not
slippery, and the reference velocity should be decreased more rapidly.
Additionally, immediately after touchdown, a couple of seconds are required
for the base limit to be established. During this period, the reference
velocity rate limit is fixed at its maximum value. This is handled by
including time since touchdown as an input to the inference system.
The rules are now described and the fuzzy sets shown in FIGS. 2 and 3.
Reference Velocity Rules:
1. If Base Limit is High and Time is Not Early Then Reference Velocity Rate
Limit=12;
2. If Base Limit is Not High Then Reference Velocity Rate Limit=20.
Calculate Decision Variables
The following variables which are calculated to be used in subsequent
calculations: error, error rate, derivative of wheel speed (.omega.),
second derivative of wheel speed (.omega.), deviation, time since
touchdown, and time since skid. These variables are computed as follows:
error (radians/sec)=reference wheel speed-desired wheel speed;
error rate (radians/sec.sup.2)=error-previous error)/timestep;
.omega. (radians/sec.sup.2)=((.omega.-previous .omega.)/timestep;
.omega. (radians/sec.sup.3)=(.omega.-previous .omega.)/timestep;
deviation=antiskid current--base limit;
time since touchdown (seconds)=time since spinup signal is received from
simulation;
time since skid (seconds)=time since error was above one ft/sec.
Determine Change in Antiskid Current (Fuzzy Inference)
The release current is the current sent to the antiskid valve. If there is
a skid, the release current deviates significantly from the base limit.
When the skid is finished, the release current returns to the base limit.
The system uses error, error rate, and .omega. to recognize how severe the
current skid is (if there is a skid), and how to respond. For example, if
the error is small, the error rate is positive, and .omega. is negative,
the wheel is starting to go into a skid. In that case, the antiskid
current increases by a large amount, 1.5 mA. If, for example, the error is
large, the error rate is zero, and .omega. is positive, the wheel is just
starting to recover from a skid, and the antiskid current should start to
return to the base limit. In this case, the antiskid current decreases by
2.0 mA.
The rules are now described and the fuzzy sets shown in FIGS. 4A, B and C.
Antiskid Current Rules:
1. If Error is Small and Error Rate is Negative and .omega. is Negative
Then .DELTA.Current=0.9 mA.
2. If Error is Small and Error Rate is Negative and .omega. is Zero Then
.DELTA.Current=0.3 mA.
3. If Error is Small and Error Rate is Negative and .omega. is Positive
Then .DELTA.Current=-2.0 mA.
4. If Error is Small and Error Rate is Zero and .omega. is Negative Then
.DELTA.Current=1.2 mA.
5. If Error is Small and Error Rate is Zero and .omega. is Zero Then
.DELTA.Current=0.0 mA.
6. If Error is Small and Error Rate is Zero and .omega. is Positive Then
.DELTA.Current=-2.0 mA.
7. If Error is Small and Error Rate is Positive and .omega. is Negative
Then .DELTA.Current=1.5 mA.
8. If Error is Small and Error Rate is Positive and .omega. is Zero Then
.DELTA.Current=0.8 mA.
9. If Error is Small and Error Rate is Positive and .omega. is Positive
Then .DELTA.Current=-2.0 mA.
10. If Error is Large and Error Rate is Negative and .omega. is Negative
Then .DELTA.Current=1.0 mA.
11. If Error is Large and Error Rate is Negative and .omega. is Zero Then
.DELTA.Current=0.3 mA.
12. If Error is Large and Error Rate is Negative and .omega. is Positive
Then .DELTA.Current=-2.0 mA.
13. If Error is Large and Error Rate is Zero and .omega. is Negative Then
.DELTA.Current=1.5 mA.
14. If Error is Large and Error Rate is Zero and .omega. is Zero Then
.DELTA.Current=0.6 mA.
15. If Error is Large and Error Rate is Zero and .omega. is Positive Then
.DELTA.Current=-2.0 mA.
16. If Error is Large and Error Rate is Positive and .omega. is Negative
Then .DELTA.Current=1.5 mA.
17. If Error is Large and Error Rate is Positive and .omega. is Zero Then
.DELTA.Current=1.2 mA.
18. If Error is Large and Error Rate is Positive and .omega. is Positive
Then .DELTA.Current=-2.0 mA.
19. If Error is Very Large and .omega. is Positive Then .DELTA.Current=1.5
mA.
20. If Error is Very Large and Error Rate is Positive and .omega. is Not
Negative Then .DELTA.Current=3.0 mA.
Determine Gain (Fuzzy Inference)
The gain decreases the effective gain of the system during slippery
conditions, and increases the effective gain during dry conditions. The
gain ranges from a value of 2.1 for dry runway conditions to 0.8 for very
slippery runway conditions. An indication of the degree to which the
runway is slippery is provided by the base limit, as it was for the
reference velocity fuzzy inference. If the base current is low, the runway
is not slippery. If the base current level is high, then the runway is
slippery.
The rules are now described and the fuzzy sets shown in FIG. 5:
Gain Rules:
1. If Base Limit is Small Then Gain=2.1.
2. If Base Limit is Medium Then Gain=1.4.
3. If Base Limit is Small Then Gain=0.8.
Determine Change in Base Limit (Fuzzy Inference)
The base current level is the level to which the release current returns
after a skid. This permits the system to remember the approximate current
level at which a skid will occur.
The system uses the deviation to determine how the base limit will change.
When the deviation is zero or very small, the base limit ramps down
gradually. When the deviation is larger, the base limit ramps up
gradually. Additionally, when there has not been a skid for a while, the
base limit ramps down more rapidly.
There is also a rule to ensure that the base limit does not ramp up when
there are oscillations in the wheel speed signal such as those caused by
the truck oscillating. Rule six (below) is included to address this
situation. The condition of the error being moderate and .omega. being
positive is met a large part of the time during oscillations, and is not
met very much during normal operation. Therefore, rule six keeps the base
limit from ramping up during oscillations, and has little effect during
normal operation.
The rules are now described and the fuzzy sets shown in FIGS. 6, A, B, C,
and D.
Base Limit Rules:
1. If Deviation is Zero Then .DELTA.Base Limit=-0.05 mA.
2. If Deviation is Small Then .DELTA.Base Limit=0.05 mA.
3. If Deviation is Medium Then .DELTA.Base Limit=0.25 mA.
4. If Deviation is Large Then .DELTA.Base Limit=0.4 mA.
5. If Time Since Skid is Large .DELTA.Base Limit Gain =-0.3 mA.
6. If Error is Moderate and .omega. is Positive Then .DELTA.Base Limit=-1.2
mA.
Sum and Limit Base Limit
The new base limit is computed by adding the .DELTA.base limit to the
previous value of base limit. The new value for the base limit is then
limited to a minimum of 0 mA, and a maximum of 45 mA.
Sum and Limit Antiskid Current
The new antiskid current is computed by adding the .DELTA.antiskid current
to the previous value of antiskid current. This new value of antiskid
current is then limited to a minimum of the base limit, and a maximum of
55 mA.
Send Current to Valve
The antiskid current is sent as a voltage to the simulation, where it is
then sent through a valve driver to the antiskid valve.
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